The 94-year-old anti-apartheid hero was rushed to a Pretoria hospital in the early hours of Saturday.
“Former president Nelson Mandela remains in hospital, and his condition is unchanged,” the presidency said in a statement.
The government had described his condition as “serious but stable” on Saturday.
“He is receiving intensive care treatment,” presidential spokesman Mac Maharaj, who served jail time with Mandela, told AFP.
It is the fourth hospital stay in seven months for the man beloved as a global symbol of peace and forgiveness and the father of the “Rainbow Nation”.
And with his latest health scare, South Africans are beginning to come to terms with the mortality of their anti-apartheid hero and first black president.
“He has done his part. We just pray that he recovers,” said Kennedy Moraga outside a private specialist heart clinic in Pretoria, where he is believed to be receiving treatment.
Two of Mandela’s daughters and some grandchildren were spotted on Sunday entering the facility, although the government has not confirmed it is where he is being treated.
“I’ve seen my father and he’s well. He’s a fighter,” Mandela’s daughter Zindzi told Britain’s Guardian newspaper on Sunday.
Access to Mandela has been restricted to close family members in a bid to reduce the risk of further infections.
In late April, President Jacob Zuma and top party officials were photographed with an unsmiling Mandela looking exceedingly frail at his Johannesburg home.
The visit prompted allegations that the underfire ruling party was exploiting Mandela for political gain.
The ANC — facing 2014 elections — has lost much of its Mandela shine amid widespread corruption, poverty and poor public services.
The party and the government on Monday denied local media reports that they had been barred from visiting Mandela in hospital by the former leader’s entourage.
“There are general restrictions that permit only relevant people to have access,” said ANC spokesman Jackson Mthembu.
Maharaj told AFP the authorities wanted “to create a conducive environment for his recovery”.
“Close loved ones are going to him for that reason, that’s all, nothing else,” he said. “He is receiving treatment and we want him to receive the treatment in the best condition for his family.”
“They would like to limit the flow of visitors.
“The president will visit him when it’s appropriate,” he said, adding that Zuma does not want “to invade that space willy-nilly”.
Mandela, who turns 95 next month, was back in hospital two months after being discharged in April following treatment for pneumonia.
He has not been seen in public since the World Cup final in South Africa in July 2010.
“It’s time to let him go,” was the stark front-page headline in the Sunday Times newspaper, reflecting the mood of many in the country.
While Twitter users expressed sadness and urged a quick recovery, they were also prepared for the worst.
“It’s time to let Nelson Mandela go. He has served his country. Let him rest with dignity and a legacy that will never die,” tweeted Ketha Msane.
South African pulmonologist Guy Richards told AFP that recurring pneumonia was rare unless there was previous lung damage.
“For example if you had tuberculosis, then often those damaged areas will be colonised with bacteria which are able to cause recurrent infections,” he said.
Mandela was diagnosed with early-stage tuberculosis in 1988 and also has had treatment for prostate cancer and suffered stomach ailments.
In December, Mandela spent 18 days in hospital, his longest stay since walking free from an apartheid prison in 1990.
In March he was admitted for a scheduled overnight check-up before returning later that month for 10 days suffering from pneumonia.
President Zuma in March appeared to prepare the nation for Mandela’s passing, saying it “should be thinking about” his going home.
After serving just one term as president, Mandela turned his energy to the battle against AIDS and conflict resolution, before stepping out of the public eye a decade ago at the age of 85.